Conventionally, there is proposed an air-fuel ratio control apparatus in which an exhaust air-fuel ratio of an internal combustion engine is detected, and a fuel injection a mount is controlled to achieve a target air-fuel ratio. However, in the case of a multi-cylinder internal combustion engine, variations in intake air amounts between cylinders occurs due to the shape of an intake manifold, the operation of intake valves and the like. In the case of an MPI (Multi Point Injection) system in which a fuel injection valve is provided for each cylinder, and fuel injection is individually performed, variations in fuel amounts between the cylinders occur due to the individual difference among fuel injection devices, or the like. Since the accuracy of the fuel injection amount control is deteriorated due to the variations between the cylinders, for example, in JP-8-338285A, at the time of air-fuel ratio detection by an air-fuel ratio sensor, it is specified which cylinder an exhaust as an actual detection object came from, and in each case, an air-fuel ratio feedback control is performed individually for the specified cylinder.
In JP-3-37020B, an air-fuel ratio of an exhaust collective part is detected using an air-fuel ratio sensor, and in view of a delay until the exhaust of the pertinent cylinder reaches the air-fuel ratio sensor, the fuel supply amount of the pertinent cylinder is corrected.
However, in the techniques of the above patents, when consideration is given to the fact that the exhausts of the respective cylinders are mixed in the exhaust collective part, the variations between the cylinders cannot be sufficiently resolved, and a further improvement is desired. Especially, JP-3-37020B is effective only in the case where the exhaust is regarded as being laminar in a passage direction. Incidentally, in order to obtain the air-fuel ratio for each cylinder with high accuracy, an air-fuel ratio sensor has only to be disposed at each branch pipe of an exhaust manifold. However, this requires the air-fuel ratio sensors the number of which is equal to the number of cylinders, and the cost is increased.
In Japanese Patent No. 2717744, a model is created in which an air-fuel ratio in an exhaust collective part is made a weighted average obtained by multiplying combustion histories by specified weights, internal state amounts are made the combustion histories, and an air-fuel ratio of each cylinder is detected by an observer. However, in this model, the air-fuel ratio in the exhaust collective part is determined by the finite combustion histories (combustion air-fuel ratios), and the histories must be increased in order to improve the accuracy, and there has been a fear that the amount of calculation is increased and the modeling becomes complicated.